flip flop

Question

Given the sequence 010202010 is generated from a sequential circuit of n flip-flops. And these flip-flops generate the sequence respectively. What is the minimum value of n?

1.   3
2.   4
3.   5
4.  ​​​​​​​ 6

Comments

9 different states so answer should be 4

Answer 1

we need to distinguish between 5 zeros, between two 1's, and also between two zeros.
to represent 0,1,2 two bits are enough
writing the sequence
0 - 00
1- 01
0 - 00
2 - 10
0 - 00
2 - 10
0 - 00
1 - 01
0 - 00
checkout which is repeating more number of times
 there are 5 zeros and we need to distinguish them
first zero = 000-00
2nd zero= 001-00
3rd zero = 010-00
4th zero=  011-00
5th zero = 100-00
two 1's can also be distiguished by 3 bits
two 2's can also be distiguished by 3 bits
so, 5 flipflops are needed, we capture the output only at last 2 flipflops and first 3 flipflops distingush between states
hence 5 are necessary

Comments

0-->1-->0-->2-->0-->2-->0-->1-->0
00000-->00001--> 00100-->00010-->01000-->00110-->01100-->00101-->10000
we are using 5 bits to represent each number it means 5 flipflops are present
capture output at last 2 flipflops in each clock cycle from the above sequence.
00 --> 01 --> 00 --> 10 --> 00 --> 10--> 00 --> 01--> 00 (which is 0-->1-->0-->2-->0-->2-->0-->1-->0)
isnt this what we wanted?
now why 5 bits?
each zero in the given question indicates different state. and also each 1 in the given question indicates different states,same with two 2's.
to distingush 5 zeros we need 3 bits. so we use 3 bits to distinguish 1's and 2's

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 @Prabhanjan_1 why do u wat to combinely distingush?
distingush 2 1's by 3 bits and 2 2's by 3 bits
check the sequence i gave in above comment. it will make it clear

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i got confused between repeating 1's and 2's but now clear ..

Yes nice explaination :)